Solve the following initial-value problem: cos(x) dy/dx + sin(x) y - 1 = 0, y(0) = 1

y= x + cosx

Step-by-step explanation:

now equation is in linear differential form

finding integrating factor;

I.F. =

using  y(0) = 1

1 = 0 +  c(cos 0)

c = 1

hence solution becomes

y= x + cosx

1. 3.4/4

2. 0.8/7

3. 0.5 x 3

4. 0.9 x 6

5. 10.8

6. 2.35

7. 0.567

8. 9.35

9. 0.02

10. 0.06

11. 0.16

12. 0.42

13. 0.63

14. 5.6

15. 8.1

16. 9.9

17. 0.28

18. 0.48

19. 0.27

20. 0.49

21. 0.45

22. 0.72

23. 0.9

24. 0.88

25. 0.75

26. 0.16

27. 0.328

28. 0.495

29. 0.72

30. 1.068